TIME DILATION due to Velocity

Imagine two mirrors kept parallel to each other with a photon bouncing back and forth between them. Consider this apparatus as a photon clock where one strike of the photon with each mirror counts as one tik.

In the first case, the apparatus is observed on the ground by a man who is stationary relative to it. In the second case, the apparatus is carried on a plane moving at a certain velocity relative to the man.

The photon clock as observed by the person on the plane.

Now, consider the man standing on the ground and observing the photon clock on the moving plane. As the plane is moving forward, it would appear to the man that the photon is not just bouncing up and down but also moving along with the plane.

The photon appears to move in this manner for the man on the ground observing the photon clock on the moving plane.

So, let during each tik of the photon clock the plane moves forward by ‘x’ m (or the velocity of the plane is x m/tik). so, the man on the ground would observe that after each strike or after each tik of the photon clock, the photon has to move ‘x’ m forward to reach and strike the other mirror. This means the distance that light has to travel has increased in the inertial frame of reference of the man on the ground.

Now, as special relativity had already proved the speed of light is constant for all observers and as in this case, the distance travelled by light increases, this could only mean that the time elapsed between two consecutive tiks decreases according to the man on the ground. (As velocity=distance/time, if velocity is constant and distance increases, the time is bound to decrease) It would appear to him that the photon clock is moving slower than normal. In fact everything on the plane would appear to be moving slowly according to him because the effect observed by him in the photon clock would also apply to everything else on the plane (as the whole plane itself is moving at a constant velocity).  Time would appear to have slowed down inside the plane!

So, what he would be observing is the result of time dilation due to relative velocity. It states that time slows down for an object moving with a relative velocity (as in this case the plane is moving relative to the man). 

It’s spooky but is tested and true.

Click Here for ‘Time dilation due to gravity’